The Affordable Care Act
Difference-in-Differences
ACA Data
Medicaid Expansion and Prevalence of Health Insurance

Background on the Affordable Care Act

Background

What percent of people are uninsured?

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# What percent of people are uninsured?

Background

What percent of people are uninsured?
How do people get health insurance?

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# How do people get health insurance?

Employer provided insurance

The U.S. still relies heavily on private insurance provided by employers.

Any thoughts on why?
# Employer provided insurance
1. Stabalization act of 1942 (wages frozen but not benefits)
2. Tax exclusion for insurance expenditures (1954)

How did the ACA change things?

Create health insurance exhanges
- Individual mandate (since set to $0)
- Premium and cost-sharing subsidies (some unpaid by Trump administration)
- Insurance subsidies (removed before intended)
- Decision assistance
- Minimum benefits and community ratings

Stay on parent’s plan to 26

Change in Insurance Type over Time

What does the literature say

The Kaiser Family Foundation has some great info on this…
- KFF Medicaid Coverage - KFF Report on ACA Expansion - Health Insurance and Mortality (not what we’re discussing here but still important)

Difference-in-Differences

Setup

[:col_header , Post-period, Pre-period] [:col_row Treated, $E(Y_{1}(1)|W=1)$, $E(Y_{0}(0)|W=1)$] [:col_row Control, $E(Y_{0}(1)|W=0)$, $E(Y_{0}(0)|W=0)$]

Strategy 1: Estimate $E[Y_{0}(1)|W=1]$ using $E[Y_{0}(0)|W=1]$ (before treatment outcome used to estimate post-treatment)

Setup

[:col_header , Post-period, Pre-period] [:col_row Treated, $E(Y_{1}(1)|W=1)$, $E(Y_{0}(0)|W=1)$] [:col_row Control, $E(Y_{0}(1)|W=0)$, $E(Y_{0}(0)|W=0)$]

Strategy 3: DD estimate…

Estimate $E[Y_{1}(1)|W=1] - E[Y_{0}(1)|W=1]$ using $E[Y_{0}(1)|W=0] - E[Y_{0}(0)|W=0]$ (pre-post difference in control group used to predict difference for treatment group)

Estimation

Key identifying assumption is that of parallel trends

\[E[Y_{0}(1) - Y_{0}(0)\|W=1] = E[Y_{0}(1) - Y_{0}(0)\|W=0]\]
# Estimation Sample means: \[\begin{align} E[Y_{1}(1) - Y_{0}(1)\|W=1] &=& \left( E[Y(1)\|W=1] - E[Y(1)\|W=0] \right) \\ & & - \left( E[Y(0)\|W=1] - E[Y(0)\|W=0]\right) \end{align}\]

Estimation

Regression:
$Y_{i} = \alpha + \beta W_{i} + \lambda 1(Post) + \delta W_{i} \times 1(Post) + \varepsilon$

[:col_header , After, Before, After - Before] [:col_row Treated, $\alpha + \beta + \lambda + \delta$, $\alpha + \beta$, $\lambda + \delta$] [:col_row Control, $\alpha + \lambda$, $\alpha$, $\lambda$] [:col_row Treated - Control, $\beta + \delta$, $\beta$, $\delta$]

Mean differences

dd.means <- dd.dat %>% group_by(w, t) %>% summarize(mean_y = mean(y.out))
knitr::kable(dd.means, col.names=c("Treated","Post","Mean"), format="html")

Treated	Post	Mean
FALSE	FALSE	1.522635
FALSE	TRUE	3.002374
TRUE	FALSE	4.515027
TRUE	TRUE	12.004623

Regression estimator

dd.est <- lm(y.out ~ w + t + w*t, data=dd.dat)
summary(dd.est)

## 
## Call:
## lm(formula = y.out ~ w + t + w * t, data = dd.dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0038 -0.6674  0.0047  0.6609  3.6135 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.52263    0.01970   77.28   <2e-16 ***
## wTRUE        2.99239    0.02795  107.07   <2e-16 ***
## tTRUE        1.47974    0.02786   53.10   <2e-16 ***
## wTRUE:tTRUE  6.00986    0.03953  152.05   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9881 on 9996 degrees of freedom
## Multiple R-squared:  0.9433, Adjusted R-squared:  0.9433 
## F-statistic: 5.543e+04 on 3 and 9996 DF,  p-value: < 2.2e-16

Insurance Data and Medicaid Expansion

Data sources

Code and links available at the Insurance Access GitHub repository

Insurance status and source

Data from the American Community Survey
CPS data also available but questions changed in 2014
Easiest way to access ACS data is through a Census API and the acs package…details on the GitHub repo

Summary stats

And now for some basic summary stats (pooling all years):

stargazer(as.data.frame(ins.dat %>% select(perc_unis, perc_direct, perc_medicaid)), type="html")

## Error: Can't subset columns that don't exist.
## [31mx[39m The column `perc_unis` doesn't exist.

Uninsurance over time

Direct purchase over time

Medicaid enrollment over time

Medicaid expansion and health insurance?

Research design

Use pre/post and expansion/non-expansion states to identify effect of Medicaid expansion: \[y_{it} = \alpha + \beta \times 1(Post) + \gamma \times 1(Expand) + \delta \times 1(Post) \times 1(Expand) + \varepsilon\]

Checking pre-trends

First just plot seperately by group:

ins.plot.dat <- ins.dat %>% filter(!is.na(expand_ever)) %>%
  group_by(expand_ever, year) %>% summarize(mean=mean(perc_unins))
  
ggplot(data=ins.plot.dat, aes(x=year,y=mean,group=expand_ever,linetype=expand_ever)) + 
  geom_line() + geom_point() + theme_bw() +
  geom_vline(xintercept=2013.5, color="red") +
  geom_text(data = ins.plot.dat %>% filter(year == 2016), 
            aes(label = c("Non-expansion","Expansion"),
                x = year + 1,
                y = mean)) +
  guides(linetype=FALSE) +
  labs(
    x="Year",
    y="Fraction Uninsured",
    title="Share of Uninsured over Time"
  )

Event study

This is poorly named: - In finance, even study is just an interrupted time series - In economics, we usually have a treatment/control group and a break in time

Event study

Second, run regression with full set of interactions and group/year dummies:

event.ins.reg <- lm(perc_unins ~ expand_2012 + expand_2014 + 
                      expand_2015 + expand_2016 + expand_2017 + 
                      expand_2018 + factor(year) + factor(State), data=event.dat)
point.est <- as_tibble(c(event.ins.reg$coefficients[c("expand_2012","expand_2014","expand_2015",
                                            "expand_2016","expand_2017","expand_2018")]),
                       rownames = "term")
ci.est <- as_tibble(confint(event.ins.reg)[c("expand_2012","expand_2014","expand_2015",
                                   "expand_2016","expand_2017","expand_2018"),],
                    rownames = "term")

Event study

Finally, plot coefficients and confidence intervals

Fixed Effects?

Recall our original regression specification:
$y_{it} = \alpha + \beta \times 1(Post) + \gamma \times 1(Expand) + \delta \times 1(Post) \times 1(Expand) + \varepsilon$

This is a special case of a general fixed effects estimator:
$y_{it} = \alpha + \delta W_{it} + \gamma_{i} + \gamma_{t} + \varepsilon$,
where $\gamma_{i}$ and $\gamma_{t}$ denote a set of coefficients on state ($i$) and year ($t$) dummy variables (or fixed effects).

Equivalence

DD is just a special case of the fixed effects approach.

summary(lm(perc_unins ~ post + expand_ever + post*expand_ever, data=ins.dat.2014))

## 
## Call:
## lm(formula = perc_unins ~ post + expand_ever + post * expand_ever, 
##     data = ins.dat.2014)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.115667 -0.027106 -0.006804  0.027765  0.117597 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               0.213965   0.007180  29.799  < 2e-16 ***
## postTRUE                 -0.054068   0.008496  -6.364 7.22e-10 ***
## expand_everTRUE          -0.046326   0.009166  -5.054 7.48e-07 ***
## postTRUE:expand_everTRUE -0.018403   0.010845  -1.697   0.0908 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04187 on 304 degrees of freedom
##   (7 observations deleted due to missingness)
## Multiple R-squared:  0.4995, Adjusted R-squared:  0.4946 
## F-statistic: 101.1 on 3 and 304 DF,  p-value: < 2.2e-16

]

summary(felm(perc_unins ~ treat | factor(State) + factor(year), data=ins.dat.2014))

## 
## Call:
##    felm(formula = perc_unins ~ treat | factor(State) + factor(year),      data = ins.dat.2014) 
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.042349 -0.007307 -0.000520  0.007342  0.039814 
## 
## Coefficients:
##        Estimate Std. Error t value Pr(>|t|)    
## treat -0.018403   0.003702  -4.971 1.22e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01429 on 257 degrees of freedom
##   (7 observations deleted due to missingness)
## Multiple R-squared(full model): 0.9507   Adjusted R-squared: 0.9411 
## Multiple R-squared(proj model): 0.0877   Adjusted R-squared: -0.08979 
## F-statistic(full model):99.11 on 50 and 257 DF, p-value: < 2.2e-16 
## F-statistic(proj model): 24.71 on 1 and 257 DF, p-value: 1.22e-06

]

Section 6: Difference-in-Differences and Effects of Medicaid Expansion

Ian McCarthy | Emory University

Econ 470 & HLTH 470

Table of contents

Background on the Affordable Care Act

Background

Background

Employer provided insurance

How did the ACA change things?

Change in Insurance Type over Time

What does the literature say

Difference-in-Differences

Setup

Setup

Estimation

Estimation

Mean differences

Regression estimator

Insurance Data and Medicaid Expansion

Data sources

Insurance status and source

Summary stats

Uninsurance over time

Direct purchase over time

Medicaid enrollment over time

Medicaid expansion and health insurance?

Research design

Checking pre-trends

Event study

Event study

Event study

Fixed Effects?

Equivalence